Take-Home Group Assignment

# Install required libraries
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In R CMD INSTALL

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# Install required libraries
data <- read.csv("data/realis2018.csv")
head(data)

Problem Description

One day, your mum tells you that we just won the first prize of TOTO which worth 2,500,000 SGD. After you discuss with your family, you decide to buy a flat and plan for the investment. During the period of time, you contact the company “Property Master@” to discuss more on the historical transaction of Singapore property. The sample data givenis “realis2018.csv”. For problems stated below, we use α= 5%.

# clean data

# filter no. of units = 1 cos some transactions are the whole damn building
data %<>% filter(No..of.Units==1)

# recode YISHUN and Yishun
data$Planning.Area <- recode(data$Planning.Area,"YISHUN"="Yishun")

Problem 1

You look around few different planning areas (Column R). When you ask the agent what is the mean Unit price(psm) for Newton flats (Column G), she claims that the mean is higher than 26500. Do you agree with your agent’s suggestion? Explain and justify your answer.

Assumptions:

• Assume “Flat” means either Condominium, Executive Condominium or Apartment
• Data is a sample of housing prices in 2018

Code

Newton <-  data %>%  filter(Planning.Area=="Newton",Property.Type %in% c("Condominium", "Apartment", "Executive Condominium"), No..of.Units == "1")
head(Newton)

z.test(Newton$Unit.Price....psm, alternative = "greater", mu= 26500,sigma.x=sd(Newton$Unit.Price....psm))

    One-sample z-Test

data:  Newton$Unit.Price....psm
z = 1.881, p-value = 0.02998
alternative hypothesis: true mean is greater than 26500
95 percent confidence interval:
 26598.75      Inf
sample estimates:
mean of x 
 27286.51 

Detailed Analysis

At 95% Confidence level, we have sufficient evidence to say that the mean price per square meter(psm) of flats in the Newton Area is more than $26500.

Problem 2

Your friend told you that Newton planning area may not be the best area to choose. He suggested you to consider other planning areas. This is a very difficult decision since you need to conduct a more comprehensive analysis and you also need to justify whether you still choose Newton or another planning area.

Assumptions:

• Assume no preference for planning area
• Assume purchasing in Q1 2020
• The budget is 2.5 million
• Assume “Flat” means either Condominium, Executive Condominium or Apartment
• Key factors to consider: Accesibility, Estate Maturity
• Metric for evaluation is PSM
• areas talked about will be by Planning Area

Code

Distribution of Properties <= 2.5 Million across Planning Areas

realis <- fread('data/realis2018.csv')
realis$pa <- toupper(realis$`Planning Area`)
centroids <- readOGR("data/MP14_PLNG_AREA_WEB_PL.shp")

OGR data source with driver: ESRI Shapefile 
Source: "D:\ASSR\TakeHome\data\MP14_PLNG_AREA_WEB_PL.shp", layer: "MP14_PLNG_AREA_WEB_PL"
with 55 features
It has 12 fields

dgp <-  spTransform(centroids, CRS("+proj=longlat +ellps=GRS80"))
one_unit <- subset(realis, realis$`No. of Units` == 1 & realis$`Transacted Price ($)` <= 2500000)
pa_units <- aggregate(realis$`No. of Units`,
                      by = list(realis$pa),
                      FUN = sum)
colnames(pa_units) = c('PA', 'Units')
m <- merge(dgp,pa_units, by.x ='PLN_AREA_N', by.y = 'PA')

pal <-
  colorBin(palette = brewer.pal(10,"YlGnBu"),
           domain = c(0,2000),
           na.color = "#00000000",
           bins=c(0,5,10,50,100,200,400,600,800,1000,1200,1400,1600,1800,2000))

n too large, allowed maximum for palette YlGnBu is 9
Returning the palette you asked for with that many colors

# create the base map, default will be openstreetmap if not selected 
# added centroids point as well
leaflet(dgp) %>% addTiles() %>% 
                 addPolygons(fillColor = ~pal(m$Units),
                             weight = 2,
                             opacity = 1,
                             color = "grey",
                             dashArray = "1",
                             fillOpacity = 0.8) %>% 
                 addLegend("topright", pal, values=(0:2000), 
                           title = "Transacted Units", 
                           labFormat = labelFormat(suffix = " Units", between = '-')) 

pa_units[order(-pa_units$Units),]

Available Flats by Planning Area

Total Stock

stock_data <- fread("data/stock2019Q4.csv")
stock_data$PA <- toupper(stock_data$PA)
stock <- merge(dgp,stock_data, by.x ='PLN_AREA_N', by.y = 'PA')

pal <-
  colorBin(palette = brewer.pal(10,"YlGnBu"),
           domain = c(0,2000),
           na.color = "#00000000",
           bins=c(0,500,1000,3000,5000,8000,10000,15000,20000,30000))

n too large, allowed maximum for palette YlGnBu is 9
Returning the palette you asked for with that many colors

# create the base map, default will be openstreetmap if not selected 
# added centroids point as well
leaflet(dgp) %>% addTiles() %>% 
                 addPolygons(fillColor = ~pal(stock$Total),
                             weight = 2,
                             opacity = 1,
                             color = "grey",
                             dashArray = "1",
                             fillOpacity = 0.8) %>% 
                 addLegend("topright", pal, values=(0:2000), 
                           title = "Total Stock", 
                           labFormat = labelFormat(suffix = " Units", between = '-')) 

stock_data[order(-stock_data$Total),]

ANOVA and Tukey on PSM per Planning Area for each Flat Type

PropType <- unique(data$Property.Type)
for (k in 1:length(unique(data$Property.Type))){
  data_property <-  data %>%  filter(Property.Type==unique(data$Property.Type)[k])
    res.aov <- aov(Unit.Price....psm.~Planning.Area,data=data_property)
    summary(res.aov)
    results <-  tidy(TukeyHSD(res.aov,ordered=TRUE))
    results_sorted <-  results %>% separate(comparison, c("Bigger", "Smaller"),sep = "-")
    
  
    rankings1 <-  results_sorted %>%  group_by(Bigger) %>%  summarise(Count=n()) %>%  arrange(desc(Count))
    rankings2 <- results_sorted %>% filter(Smaller %!in% rankings1$Bigger) %>%  group_by(Smaller) %>% summarise(Count=n())%>%  arrange(Count)
    names(rankings2)[1] <- "Bigger"
    rankings <- rbind(rankings1,rankings2)

    rankings$Rank <-  seq.int(nrow(rankings)) 
    rankings %<>% dplyr::select(-Count)
    results_sorted <- left_join(results_sorted, rankings) %>%  arrange(Rank)

 
    rankings$TukeyRank <- NA
    rankings$TukeyRank[1] <- 1
    for( i in 2:nrow(rankings)){
      if(results_sorted$adj.p.value[results_sorted$Bigger==rankings$Bigger[i-1]&results_sorted$Smaller == rankings$Bigger[i]]<=0.05){
        rankings$TukeyRank[i] <- rankings$TukeyRank[i-1]+1
      } else if(sum((results_sorted$Smaller[results_sorted$Bigger==rankings$Bigger[i-1]&results_sorted$adj.p.value<=0.05] %in% results_sorted$Smaller[results_sorted$Bigger==rankings$Bigger[i]&results_sorted$adj.p.value>0.05])>0)){
        rankings$TukeyRank[i] <- rankings$TukeyRank[i-1]+1
       } else {
         rankings$TukeyRank[i] <- rankings$TukeyRank[i-1]
       }
     }
    
    Tukey_ranked <-  rankings %>%  dplyr::select(Bigger,TukeyRank)
    names(Tukey_ranked)[1] <-  "Planning.Area"
    Planning_Mean <-  data_property %>% group_by(Planning.Area) %>%  summarise(mean= mean(Unit.Price....psm.), sd= sd(Unit.Price....psm.))
    Tukey_ranked <- left_join(Tukey_ranked, Planning_Mean)
    
    assign(paste("aov_", PropType[k], sep = ""), tidy(res.aov))
    assign(paste("Tukey_", PropType[k], sep = ""), as.data.frame(Tukey_ranked))
}

Joining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vector

head(Tukey_Apartment)

head(Tukey_Condominium)

head(`Tukey_Executive Condominium`)

head(`Tukey_Detached House`)

head(`Tukey_Semi-Detached House`)

head(`Tukey_Terrace House`)

summary(res.aov)

                Df    Sum Sq   Mean Sq F value Pr(>F)    
Planning.Area   14 2.071e+09 147906034   216.6 <2e-16 ***
Residuals     1731 1.182e+09    682842                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#Detailed analysis 

#We performed the ANOVA test to determine if all the mean PSM per planning areas were similar.
#At 95% Confidence level, as P value is less than 0.05, we have sufficient evidence to say to reject H0 and that the mean price per square meter(psm) of flats are significantly different
#To compare the group means, a post hoc test -  TUKEY test - was performed per property type 
#Given the extensive results output, the TUKEY results were sorted for clarity. 
#For each property type, the differences were sorted, filtered for results with adjusted p-value <=0.05 and then ranked accordingly 
#At 95% confidence intervals:
#   For property type - apartments - Orchard has the most significantly differences between means in PSM. River Valley, Newton and Downtown Core are ranked 2nd.
#   For property type - Condominium - Orchard and River Valley have the most significantly different differences between means in PSM. The Newton area came in 2nd.
#   For property type - EC - Bishan has the most significantly different differences between means in PSM.Sengkang, Punggol came in 2nd.
#   For property type - Detached House - Newton has the most significantly different differences between means in PSM. Tanglin and Novena / Southern islands (Sentosa) are ranked 2nd and 3rd respectively
#   For property type - Semi-Detached House - the River Valley area has the most significantly different differences between means in PSM. Tanglin and Marine Parade are joint 2nd.
#   For property type - Terrance House - Newton has the most significantly different differences between means. Rochor, River Valley and Novena are joint 2nd. 

ANOVA and Tukey on Transacted Price per Planning Area for each Flat Type

# output the damn tukey table and sort
# jayne do anova



for (k in 1:length(unique(data$Property.Type))){
  data_property <-  data %>%  filter(Property.Type==unique(data$Property.Type)[k])
    res.aov <- aov(Transacted.Price....~Planning.Area,data=data_property)
    summary(res.aov)
    results <-  tidy(TukeyHSD(res.aov,ordered=TRUE))
    results_sorted <-  results %>% separate(comparison, c("Bigger", "Smaller"),sep = "-")
    
  
    rankings1 <-  results_sorted %>%  group_by(Bigger) %>%  summarise(Count=n()) %>%  arrange(desc(Count))
    rankings2 <- results_sorted %>% filter(Smaller %!in% rankings1$Bigger) %>%  group_by(Smaller) %>% summarise(Count=n())%>%  arrange(Count)
    names(rankings2)[1] <- "Bigger"
    rankings <- rbind(rankings1,rankings2)

    rankings$Rank <-  seq.int(nrow(rankings)) 
    rankings %<>% dplyr::select(-Count)
    results_sorted <- left_join(results_sorted, rankings) %>%  arrange(Rank)

 
    rankings$TukeyRank <- NA
    rankings$TukeyRank[1] <- 1
    for( i in 2:nrow(rankings)){
      if(results_sorted$adj.p.value[results_sorted$Bigger==rankings$Bigger[i-1]&results_sorted$Smaller == rankings$Bigger[i]]<=0.05){
        rankings$TukeyRank[i] <- rankings$TukeyRank[i-1]+1
      } else if(sum((results_sorted$Smaller[results_sorted$Bigger==rankings$Bigger[i-1]&results_sorted$adj.p.value<=0.05] %in% results_sorted$Smaller[results_sorted$Bigger==rankings$Bigger[i]&results_sorted$adj.p.value>0.05])>0)){
        rankings$TukeyRank[i] <- rankings$TukeyRank[i-1]+1
       } else {
         rankings$TukeyRank[i] <- rankings$TukeyRank[i-1]
       }
     }
    
    Tukey_ranked <-  rankings %>%  dplyr::select(Bigger,TukeyRank)
    names(Tukey_ranked)[1] <-  "Planning.Area"
    Planning_Mean <-  data_property %>% group_by(Planning.Area) %>%  summarise(mean= mean(Transacted.Price....), sd= sd(Transacted.Price....))
    Tukey_ranked <- left_join(Tukey_ranked, Planning_Mean)
    
    assign(paste("aov_", PropType[k], sep = ""), tidy(res.aov))
    assign(paste("Tukey_", PropType[k], sep = ""), as.data.frame(Tukey_ranked))
}

Joining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vectorJoining, by = "Bigger"
Joining, by = "Planning.Area"
Column `Planning.Area` joining character vector and factor, coercing into character vector

head(Tukey_Apartment)

head(Tukey_Condominium)

head(`Tukey_Executive Condominium`)

head(`Tukey_Detached House`)

head(`Tukey_Semi-Detached House`)

head(`Tukey_Terrace House`)

summary(res.aov)

                Df    Sum Sq   Mean Sq F value Pr(>F)    
Planning.Area   14 1.689e+13 1.206e+12   65.86 <2e-16 ***
Residuals     1731 3.170e+13 1.831e+10                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#Detailed analysis 

#We performed the ANOVA test to determine if the mean transacted price per planning areas were similar.
#At 95% Confidence level, as P value is less than 0.05, we have sufficient evidence to say to reject H0 and that the mean transacted price of flats are significantly different
#To compare the group means, a post hoc test -  TUKEY test - was performed for each property type 
#Given the extensive results output, the TUKEY results were sorted for clarity. 
#For each property type, the differences were sorted, filtered for results with adjusted p-value <=0.05 and then ranked accordingly 
#At 95% confidence intervals:
#   For property type - apartments - Orchard has the most significantly different differences between means in transacted prices. Newton and Downtown core are ranked 2nd. 
#   For property type - Condominium - Newton and Tanglin have the most significantly different differences between means in transacted prices. Orchard and River Valley come in 2nd.
#   For property type - EC - the Bishan has the most significantly different differences between means in transacted prices. Ang Mo Kio and Bukit Batok are ranked 2nd and 3rd respectively.
#   For property type - Detached House - Newton has the most significantly different differences between means in transacted prices. Tanglin and Southern islands (Sentosa) / Bukit Timah / Novena / Marine Parade are ranked 2nd and 3rd respectively.
#   For property type - Semi-Detached House - Tanglin has the most significantly different differences between means in transacted prices. River Valley is ranked 2nd.
#   For property type - Terrance House - Newton has the most significantly different differences between means in transacted prices. Tanglin and Novena areas are joint 2nd. 

MRT Stations (Existing and Planned) by Planning Area

mrt <- read.csv("data/Planning_area_mrt_stations.csv")
mrt$Planning.Area <- toupper(mrt$ï..Planning.Area)
dgp <-  centroids <- readOGR("data/MP14_PLNG_AREA_WEB_PL.shp")

OGR data source with driver: ESRI Shapefile 
Source: "D:\ASSR\TakeHome\data\MP14_PLNG_AREA_WEB_PL.shp", layer: "MP14_PLNG_AREA_WEB_PL"
with 55 features
It has 12 fields

dgp <-  spTransform(dgp, CRS("+proj=longlat +ellps=GRS80"))
mrt2 <- merge(dgp,mrt, by.x ='PLN_AREA_N', by.y = 'Planning.Area')

#All MRT Stations
mrt_pal <- colorFactor(palette= brewer.pal(15, 'RdYlGn'),
                        domain=c(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14),
                        na.color = "#00000000")

n too large, allowed maximum for palette RdYlGn is 11
Returning the palette you asked for with that many colors

 
leaflet(dgp) %>% addTiles() %>% addPolygons(fillColor = ~mrt_pal(mrt2$Total.no..of.stations),
                                            weight = 2,
                                            opacity = 1,
                                            color = "grey",
                                            dashArray = "1",
                                            fillOpacity = 0.8) %>% addLegend("topright", mrt_pal, values=(0:14), title= "MRT Stations", labFormat = 
                                                                               labelFormat(suffix = " stations"))

#Only current MRT stations
mrt_pal2 <- colorFactor(palette= brewer.pal(12, 'RdYlGn'),
                        domain=c(0,1,2,3,4,5,6,7,8,9,10,11),
                        na.color = "#00000000")

n too large, allowed maximum for palette RdYlGn is 11
Returning the palette you asked for with that many colors

leaflet(dgp) %>% addTiles() %>% addPolygons(fillColor = ~mrt_pal2(mrt2$No..of.operational.stations),
                                            weight = 2,
                                            opacity = 1,
                                            color = "grey",
                                            dashArray = "1",
                                            fillOpacity = 0.8) %>% addLegend("topright", mrt_pal2, values=(0:11), title= "MRT Stations", labFormat = 
                                                                               labelFormat(suffix = " stations"))

NA

Detailed Analysis

#The optimal planning area(s) to purchase will depend on what we want out of the the property. If we are looking to purchase an upscale Flat for investment purposes, Newton could be an option but the mean prices are high and mostly beyond our budget. There is also only 1 MRT station and the properties available are limited. A better alternative planning area would be River Valley as it has one of the highest number of available “Apartments” within $2.5 million. Although accessibility of River Valley is lower than some planning areas with only 1 MRT station, it has 2 more future MRT stations planned (potentially increasing the value) and it is relatively close to the CBD. #If we are looking to buy a flat to live in, we will be more concerned sbout the accessibility as well as affordability. In this regard, we would prefer planning areas like Bedok or Toa Payoh as they are mature estates with high levels of accessibility and amenities. Both Toa Payoh and Bedok have a Integrated Transport Hub and relatively high number of MRT stations, with Bedok having a total of 11 MRT stations (current and future) in total. In addition, the apartments are relatively affordable (xxx and yyy) and we could even purchase 2 if we wanted to. #Alternatively, if we are simply looking for a larger space at the cheapest possible rates and save the rest of the money for other purposes, the best planning areas would be Jurong East or Jurong West as they have the lowest psm (www and zzz). In addition, there are multiple malls available and decent accessibility (bus interchange and MRT). There will be a total of 15 MRT stations in the area in the near future.